Name some bitwise operations you know

Bitwise operations are fundamental operations that directly manipulate individual bits of binary numbers. Here are some common bitwise operations:

1. Bitwise AND (&)

• Description: Takes two binary numbers and performs a logical AND operation on each pair of corresponding bits. The result is 1 only if both bits are 1.
• Example:
  $$
  12 & 25 \rightarrow 00001100 & 00011001 = 00001000 \text{ (8 in decimal)}
  $$
• Use Case: Often used for bit masking to check if specific bits are set.

2. Bitwise OR (|)

• Description: Takes two binary numbers and performs a logical OR operation on each pair of corresponding bits. The result is 1 if at least one of the bits is 1.
• Example:
  $$
  12 | 25 \rightarrow 00001100 | 00011001 = 00011101 \text{ (29 in decimal)}
  $$
• Use Case: Used to set specific bits in a number.

3. Bitwise XOR (^)

• Description: Takes two binary numbers and performs a logical XOR operation on each pair of corresponding bits. The result is 1 if the bits are different.
• Example:
  $$
  12 \oplus 25 \rightarrow 00001100 \oplus 00011001 = 00010101 \text{ (21 in decimal)}
  $$
• Use Case: Used in algorithms for swapping values without a temporary variable and for error detection in data transmission.

4. Bitwise NOT (~)

• Description: Takes a single binary number and inverts all the bits (0 becomes 1 and 1 becomes 0).
• Example:
  $$
  \sim 12 \rightarrow \sim 00001100 = 11110011 \text{ (-13 in decimal, considering two's complement representation)}
  $$
• Use Case: Used to flip all bits in a number.

5. Left Shift (<<)

• Description: Shifts the bits of a number to the left by a specified number of positions. Each shift to the left is equivalent to multiplying the number by 2.
• Example:
  $$
  12 << 2 \rightarrow 00001100 << 2 = 00110000 \text{ (48 in decimal)}
  $$
• Use Case: Used for efficient multiplication by powers of 2.

6. Right Shift (>>)

• Description: Shifts the bits of a number to the right by a specified number of pos...